This thesis is concerned with the detection of very high energy cosmic gamma-rays from isolated pulsars and X-ray binary sources using the atmospheric Cerenkov technique. A general introduction to gamma ray detection techniques is followed by adscription of the properties of atmospheric Cerenkov radiation and a discussion of the principles of the atmospheric Cerenkov technique. The Mark I and Mark II gamma-ray telescopes operated in Dugway, Utah by the University of Durham between 1981 and 1984 are briefly described. There follows a discussion of the results from observations at many different wavelengths of Cygnus X-3. This object was observed by the Durham group between 1981 and 1983 in Dugway Utah and also in Durham during autumn 1985. The detection in the Dugway data of the 4.8 hr X-ray period and the possible detection of a19.2 day intensity variation are considered. The discovery of a 12.59 ms pulsar in data taken on Cygnus X-3 in 1983 is described. Evidence is presented which suggests this periodicity is also present at a weaker level in earlier data and also in the data taken in Durham in 1985.Results from observations of PSR1937+21 , PSR1953+29and six radio pulsars , are presented. The design and construction of the Mark III telescope, now operating in Narrabri , N.S.W. , is described in detail. Preliminary results from observations with the Mark III telescope of three objects, LMC X-4, the Vela pulsar and CentaurusX-3, are presented, with particular reference to periodicities inherent in the sources. An observation of the supernova in the Large Magellanic Cloud is discussed. A brief discussion of the mechanisms by which V.H.E. gamma-rays may be produced in isolated pulsars and X-ray binary pulsars is given, followed by a description of the future prospects for the Mark III and Mark IV telescopes.